Deep networks learn to parse uniform-depth context-free languages from local statistics

TL;DR

This paper investigates how deep neural networks, including convolutional and transformer models, learn to parse uniform-depth context-free languages from local statistical cues, revealing the role of data correlations in hierarchical structure learning.

Contribution

The paper introduces a tunable class of probabilistic context-free grammars and an inference algorithm linking learnability to language statistics, validated across multiple neural architectures.

Findings

Correlations at different scales facilitate hierarchical representation learning.

Deep networks can parse context-free languages using local statistics.

Sample complexity depends on language ambiguity and correlation structure.

Abstract

Understanding how the structure of language can be learned from sentences alone is a central question in both cognitive science and machine learning. Studies of the internal representations of Large Language Models (LLMs) support their ability to parse text when predicting the next word, while representing semantic notions independently of surface form. Yet, which data statistics make these feats possible, and how much data is required, remain largely unknown. Probabilistic context-free grammars (PCFGs) provide a tractable testbed for studying these questions. However, prior work has focused either on the post-hoc characterization of the parsing-like algorithms used by trained networks; or on the learnability of PCFGs with fixed syntax, where parsing is unnecessary. Here, we (i) introduce a tunable class of PCFGs in which both the degree of ambiguity and the correlation structure across scales can be controlled; (ii) provide a learning mechanism -- an inference algorithm inspired by the structure of deep convolutional networks -- that links learnability and sample complexity to specific language statistics; and (iii) validate our predictions empirically across deep convolutional and transformer-based architectures. Overall, we propose a unifying framework where correlations at different scales lift local ambiguities, enabling the emergence of hierarchical representations of the data.